<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">S</font> =  <a href="waybel18.html#K9">Sierpinski_Space</a> ;<br/>
<a NAME="E1:3_1_1"/>
 ex <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <a href="waybel18.html#K9">Sierpinski_Space</a>  st  <a href="pre_topc.html#K4">Cl</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">p</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">p</font></span><a href="domain_1.html#K6">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:3_1_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <a href="waybel18.html#K9">Sierpinski_Space</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">0,1</span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="waybel18.html#D9">WAYBEL18:def 9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">p</font> = 1 as   <a href="pre_topc.html#NM2">Point</a> of <a href="waybel18.html#K9">Sierpinski_Space</a>  <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon">p</font>
;<br/>

<b>thus </b><a NAME="E3:3_1_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">p</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">p</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:3_1_1"/>
not  <a href="waybel18.html#K9">Sierpinski_Space</a>  is <a href="urysohn1.html#V1">being_T1</a>
 <b>by </b><i><a class="ref" href="yellow_8.html#T35">YELLOW_8:35</a></i>;<br/>


</div>
